1. Field of Invention
This invention relates to vector-wave characterizations, specifically to the determination of the relative phases among the wave's vector components, the wave's polarization, and the direction of the wave's source.
2. Background of the Invention
In many practical situations, one needs to know the relative phases among the sinusoidally time-varying components of a vector. This vector often arises from the propagation of a vector-wave (such as an electromagnetic wave, as opposed to a scalar wave such as a sound wave). The determination of the polarization characteristics of an antenna, for example, requires that the relative phases among the three spatial components of the electric field vector, as well as their amplitudes, be measured. A commonly used procedure is to find the direction (known as the null direction), projected along which the amplitude is zero; the polarization ellipse then lies in the plane (known as the polarization plane) perpendicular to this null direction. Further measurements are needed in the polarization plane to determine the shape, size, eccentricity, and other characteristics of the ellipse. The disadvantages of these measurements are well-known in the art:
(a) The null direction is found by trial and error; repeated measurements in different directions must be made until the null direction is found.
(b) These measurements must be performed sequentially; the choice of direction along which one performs the next amplitude measurement depends on the amplitudes found in previous measurements.
(c) The number of measurements in this trial-and-error method cannot be determined in advance. Moreover, additional measurements must be made in the polarization plane until one can trace out an ellipse.
(d) These measurements are time-consuming in practice, and if the wave is a transient event, the method described above is not possible.
Furthermore, the relative phases among the three spatial components of the wave vector are obtained by recording how each component changes with time with respect to a reference time-base signal (known as the "synchronizing lead"); the relative phases are then computed from time-delay measurements relative to the synchronizing lead.
(e) These time-delay measurements pose well-known practical problems at high frequencies.
(f) They are impossible at low intensity, where the quantum nature of measurements forbids it.
The relative phases among the components of a sinusoidally time-varying vector are also needed in determining the source direction of plane vector waves, and in these situations, there are no synchronizing leads.
(h) Measuring time delay of the components with respect to one selected component is unreliable in practice.
(i) Even when it is reliable, the method still fails entirely for electromagnetic field whose intensities are low enough to reveal individual photons. The failure is due to the quantum nature of light where the detection of photons is an all-or-none event, and if a photon is detected in, say, the x-direction, then no photon will be detected in the y-direction. No time delay measurement between the x- and the y-component is possible since no photon is detected in the latter component.
More generally, in quantum systems, the amplitudes are related to the probabilities of finding a particular value of a quantum number, such as spin, in a particular direction in three-dimensional space. The relative phases in this case give the orientation of the quantum state in the quantum system's Hilbert space, and give rise to interference behavior.
(j) In these quantum systems, it is impossible to measure the relative phases directly because there is no quantum "synchronizing lead".